Dimension of quasicircles

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We introduce canonical antisymmetric quasiconformal maps, which minimize the quasiconformality constant among maps sending the unit circle to a given quasicircle. As an application we prove Astala's conjecture that the Hausdorff dimension of a $k$-quasicircle is at most $1+k^2$.
Acta Mathematica, to appear

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Complex Variables, 30C62; 30C80

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http://salesiana.dossiersoluciones.com/handle/123456789/226214

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0904.1237
 http://arxiv.org/abs/0904.1237

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arXiv